AVO-preserving processing

Quantitative interpretation (QI) workflows — AVO analysis, inversion for elastic attributes, pre-stack simultaneous inversion — all depend on relative amplitudes being preserved through the processing chain. A CMP's reflection amplitude as a function of source-receiver offset encodes the reflector's intercept and gradient, which in turn encode fluid content, lithology, and porosity. Any processing step that manipulates amplitudes in an offset-dependent way destroys that signal. This section is about what those steps are, and what an amplitude-preserving flow looks like.

1. The AVO model — Shuey 2-term

For small contrasts and moderate angles (≤ 35°), Aki–Richards reduces to the 2-term Shuey approximation:

where $A = \tfrac{1}{2}(\Delta V_p/V_p + \Delta\rho/\rho)$ is the intercept (normal-incidence reflectivity) and $B = \tfrac{1}{2}\Delta V_p/V_p - 2(V_s/V_p)^2(2\Delta V_s/V_s + \Delta\rho/\rho)$ is the gradient. Extracting (A, B) per CMP is the core of AVO analysis; their joint distribution classifies reservoirs (Class I–IV per Rutherford & Williams 1989).

2. The widget

Set a true AVO curve with sliders for A and B. Pick a processing flow from the buttons below. The widget plots the true curve (teal) and the processed curve (yellow dashed), fits $\hat{A} + \hat{B}\sin^2\theta$ to the processed samples (blue dotted line), and reports the recovered parameters plus the error. The bottom line: amplitude-preserving processing gives $\hat{A}, \hat{B}$ equal to the inputs; any other flow distorts them.

3. The four processing modes

• Amplitude-preserving (ideal). No AGC, spherical divergence properly corrected, no aggressive mutes. Recovered (Â, B̂) = true (A, B). This is the target.
• AGC applied. Automatic Gain Control normalises amplitudes in a rolling time–offset window to compensate for apparent attenuation. It is widely used for visual interpretation because it makes events visible at all depths, but it completely destroys angle-dependent amplitude variation. The recovered gradient B̂ goes to zero regardless of what the true B was — every Class III anomaly becomes a flat Class I non-anomaly. If AGC appears anywhere in a QI flow, the flow is broken.
• Spherical divergence uncorrected. Spherical divergence is the geometric 1/r² amplitude decay of a wavefront. It is corrected by multiplying by $(t \cdot v^2)$ in production. If that correction is missed or wrong, far-offset amplitudes are systematically suppressed (larger raypath length → more un-corrected loss), biasing the gradient B̂ toward more negative values. Classic symptom: apparent AVO anomaly everywhere because every reflector looks like it brightens toward normal incidence.
• Aggressive stretch mute at 25°. NMO stretches far-offset samples, reducing their effective frequency. Production flows mute samples stretched past some threshold to prevent low-frequency contamination of the stack. If the mute is too aggressive (cuts below 25°), you lose all the far-offset samples that carry the AVO gradient information. B̂ becomes unreliable because the fit only has near-offset data.

4. What an amplitude-preserving flow looks like

• Source signature deconvolution. Remove the source wavelet carefully using measured far-field signatures where possible. Surface-consistent deconvolution equalises shot–receiver pairs without introducing arbitrary amplitude bias.
• Spherical divergence correction. Multiply by $t \cdot v^2_{RMS}(t)$ to compensate the geometric wavefront decay.
• Surface-consistent amplitude (SCA) balancing. Decompose amplitude variations into shot, receiver, offset, and CDP terms, remove the shot and receiver terms that reflect acquisition non-uniformities, keep the offset and CDP terms that carry geology.
• Static corrections applied without amplitude scaling — statics is a time shift, not an amplitude operation.
• Ghost deconvolution for marine data — preserves amplitudes if designed as a minimum-phase matched filter.
• Demultiple (SRME + Radon with moderate cutoff) — amplitude-preserving parameterisation is slightly looser than for imaging.
• Mild NMO with small-stretch mute (≅35° typically, not 25°).
• No AGC anywhere. Anywhere.
• Amplitude-preserving pre-stack time or depth migration (§7.2) as the final step before AVO extraction.

5. How to spot AVO distortion on real data

• Every anomaly looks like Class I (flat AVO gradient, positive intercept). Likely: AGC somewhere upstream.
• Every reflector has a strong negative gradient (apparent Class III). Likely: spherical divergence missing or wrong.
• Gradient becomes unreliable beyond some angle, fits are noisy. Likely: aggressive stretch mute.
• A known wet-sand reference reflector shows AVO. Wet sands are supposed to have near-zero gradient. If they do not, something in the flow is distorting amplitudes.

6. What to do if the flow was not amplitude-preserving

Reprocess. The damage from AGC or un-corrected spherical divergence cannot be un-done by post-processing — the information is gone. Occasionally a flow can be salvaged by stacking across a single reflector and back-inverting for a relative correction, but the cleaner and more defensible answer is to rebuild the pre-stack data from raw and apply an explicit amplitude-preserving flow from the start. Project managers resist this because reprocessing is expensive; the alternative is shipping a QI product that is inconsistent with geology, which is a worse outcome.

Where this goes next

§7.2 covers the migration step: Kirchhoff migration with proper amplitude weighting so that after migration, amplitudes still reflect the subsurface contrast rather than the operator's geometric aperture. "True-amplitude" migration, as opposed to the "structural" migration that is adequate for visual interpretation.

References

• Castagna, J. P., Backus, M. M. (1993). Offset-Dependent Reflectivity. SEG.
• Russell, B. H. (1988). Introduction to Seismic Inversion Methods. SEG.
• Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge UP.